How credible is [the claim that salmon catch has increased by over 100,000 tons]?
Let us examine both the weight and number of salmon (see ADF&G Press Releases) per year.
The fertilization was conducted in 2012. Salmon numbers are expected to fluctuate and differ for even and odd years due to the two-year spawn times of pink salmon.
For each year, the harvest of the salmon industry in Alaska is recorded by the Alaska Department of Fish and Game. For 2013, a record high of 272 million salmon was recorded. For 2015, the salmon industry also fared particularly well with 263.5 million salmon. For even years, salmon catches are lower. In 2014, the 360,000 ton harvest was comprised of 156.4 million salmon. 2016 was a record-low harvest of 110 million salmon.
The last odd-year and even-year harvests prior to the fertilization event yielded 177 million salmon and 127 million salmon for 400,000 tons and 330,000 tons, respectively.
Comparing odd years, the harvest increased by 128,000 tons. For even years, the harvest increased by 29,000 tons, which does not appear to stand out among the normal fluctuation in years.
Yes, the salmon catch increased by over 100,000 tons for the immediate odd-year harvest.
As @Murphy has pointed, correlation does not imply causation. This is 1 event, and there are natural variations in salmon levels. 13 ocean iron fertilization experiments have been conducted since 1990 (source and source) and they have primarily focused on phytoplankton levels, not salmon levels. In the Nature news article, the director of the Millennium Institute of Oceanography in Concepción, Chile is quoted as saying "[The research foundation] claim that by producing more phytoplankton, they could help the recovery of the fisheries...We don’t see any evidence to support that claim."
The second link mentions a connection between volcanic ash and salmon numbers which would seem to lend some credence but is this generally accepted?
The link between volcanic ash and salmon numbers is poorly understood. According to the National Park Service, "the longer-term effects [of volcanic activity] are also generally negative." Articles that have mentioned volcanic activity and salmon levels (in particular around 2010) are all completely theoretical.
Further study is needed before making a connection between volcanic activity and salmon levels.
Note: While this question may have been asked in June 2014 , it's still interesting to consider the implications of such iron releases. As recently as May 2017, this topic has still been proposed. Thus, an answer may be warranted.